Broadband wireless systems are in a rapidly evolutionary phase in terms of the development of various technologies, development of various applications, deployment of various services and generation of many important standards in the field. Although there are many factors to be considered in the design of these systems, the key factors have been the bandwidth utilization efficiency due to the limited bandwidth allocation, flexibility in operation and robustness of the communication link in the presence of various disturbances while achieving the specified performance. Orthogonal Frequency Division Multiple Accessing (OFDM) techniques offer efficient bandwidth utilization and provide some immunity against one of the most common type of distortion, viz., the distortion due to the multipath propagation environment. Therefore, the OFDM techniques have been adapted in many wireless communication standards, such as the World-wide Interoperability for Microwave ACCESS (Wimax), digital audio broadcasting (DAB), digital video broadcasting-terrestrial (DVB-T), Long Term Evolution (LTE), etc.
One of the advantages of the OFDM system is the mitigation of a major source of distortion present in high data rate wireless communication links, namely the inter symbol interference (ISI) achieved by reducing the symbol period by the use of multiple carrier transmission. However, the use of a large number of carriers based on the orthogonality property in the OFDM system makes the performance of the system very sensitive to any carrier frequency offsets introduced, for example, by the Doppler shifts encountered in the wireless channels. The proper operation of the OFDM system requires means for precise estimate of the Doppler that may be different for different carriers in the frequency selective fading channel, and means to mitigate such a Doppler effect from the received OFDM signal. Various methods exist in the prior art to solve this problem.
An outstanding problem arising with the use of a relatively large number N of carriers used in the OFDM signal is a relatively high peak to average power ratio resulting in a much reduced radio frequency (RF) power amplifier efficiency. Due to the inherent saturation in the RF power amplifier, the signal with amplitude exceeding the input linear range of the amplifier is clipped or distorted. In order to keep the distortion to some specified limit arrived at by the signal to distortion plus noise power ratio considerations, the output RF power is backed off from the maximum available power at the amplifier output and higher is the peak to average power ratio of the signal at the amplifier input, larger is the required back off in the output power. The output back off concurrently also results in the reduction of the DC to RF power conversion efficiency of the RF power amplifier thus increasing the drain on the battery or any other power supply source in the mobile devices. Another problem arising due to distortion caused by the amplifier is the spreading of the spectrum of the OFDM signal outside the allocated band. Thus there has been strong motivation to come up with methods to reduce the peak to average power ratio of the OFDM signal without causing any distortion in the process of transformation, or losing in terms of bandwidth or other important efficiency measures.
Among the various methods to reduce the peak to average power ratio of the OFDM signal is the clipping method wherein the signal above a certain specified value is clipped. This is similar to the clipping by the amplifier and thus introduces distortion, however, clipping and filtering the signal before inputting to the RF amplifier may mitigate the problem of spectrum spreading that is encountered by the clipping caused by the amplifier. Moreover, by using adaptive threshold in clipping some possible reduction in distortion may be achieved.
The selective mapping (SLM) method of PAPR reduction consists of forming K vectors Pq, q=1, 2, . . . , Q, for some integer Q, with the ith element of the vector Pq selected equal to Piq=exp[jφiq]; j=√{square root over (−1)}, i=0, 1, . . . , N−1 with the dimension of the modulation symbol vector X(k) equal to N. The phase φiq is selected in a random manner with a uniform probability density function over the interval [0,2π]. The set of vectors thus formed is made known to the receiver in advance. For any time k, the modulation symbol vector X(k) is component wise multiplied by each of the Q vectors Pq resulting in the modified vector Xq(k), q=1, 2, . . . , Q. This follows evaluation the inverse fast Fourier transform (IFFT) xq(k) of Xq(k) and computing the peak to average power ratio of the OFDM modulation signal vector xq(k) for q=1, 2, . . . , Q. The vector xq(k) with the minimum PAPR is selected for transmission with the corresponding index q0 made available to the receiver as a side information.
In the partial transmit sequence (PTS) method, the set of indices 0 through N−1 is partitioned into V disjoint subsets Sv, v=1, 2, . . . , V wherein each of the V subsets has (N/V) indices. For v equal to 1 through V, a vector Xv(k) of length N is obtained with all its elements equal to 0 except the ones with indices in the subset Sv that are selected to be equal to the corresponding elements of the vector X(k) resulting in
      X    ⁡          (      k      )        =            ∑              v        =        1            V        ⁢                            X          v                ⁡                  (          k          )                    .      Each of the V vectors is inverse Fourier transformed using the IFFT providing the V signal vectors xv(k)=F−1{Xv(K)} wherein F−1 denotes the inverse Fourier transform. The signal vectors are multiplied by the complex scalars exp[jφv(k)] with □v selected randomly and is uniformly distributed over the interval (0, 2□). The weighted signal vectors are summed and the PAPR of the resulting sum is computed. The PAPR is minimized over the selection of the scalars exp[jφv(k)] and the result of such a minimization is selected for transmission. The selected coefficients are provided to the receiver as a side information.
In the dummy sequence insertion (DSI) method of the PAPR reduction, the vector X(k) is comprised of NI modulation symbols and ND=(N−NI) dummy symbols resulting in X(k)=[XIT(k) XIT(k)]T wherein T denotes the matrix transpose, and XI(k) and XD(k) are the vectors of length NI and ND and comprised of the modulation symbols and dummy symbols respectively. The DSI method results in a reduction of the bandwidth efficiency by a factor of (NI/N), however, it does not require any side information. The selection of the dummy sequence is comprised of an initial step and a recursive step that modifies the dummy sequence until the PAPR of x(k)=F−1 {X(K)} is below a threshold or the number of recursions exceeds some maximum permissible number of recursions. Four different methods for the selection of the dummy sequence have been suggested in. In the first method, the dummy sequence is comprised of a complementary sequence with different complementary sequences selected in the recursive step. In another method, the initial dummy sequence is selected to be an all 0 or an all 1 sequence, with the recursion step comprised of sequentially flipping the dummy sequence bits until the PAPR below the threshold value is achieved or the number of recursions exceed a specified limit.
In the method of selective scrambling, the message bit sequence is scrambled by each of the four m-sequences that are not cyclically shifted versions of each other, with the two bits representing the index q of the m-sequence appended to the scrambled sequence. The scrambled sequences are modulated into QPSK symbols resulting in the OFDM modulation symbol vectors Xq(k) which are inverse Fourier transformed resulting in the OFDM modulated signal vectors xq(k) for q=1, 2, 3 and 3. The vector among the 4 vectors xq(k) with a minimum PAPR is selected for transmission. This method is very similar to the SMI method with the difference that it is the bit sequence that is scrambled instead of the QPSK modulation symbol sequence in the SMI method.
In the block coding schemes for the PAPR reduction, the OFDM modulation symbol vector X(k) is transformed using one of the block error correction codes. For example, the use of complementary sequence codes is taught by H. Ochiai and H. Imai, in “MDPSK-OFDM with Highly Power Efficient Block Codes for Frequency-Selective Fading Channels,” IEEE Transactions on Vehicular Technology, Vol. 49, No. 1, January 2000, pp. 74-82. While the use of the block error correction codes to reduce the PAPR while simultaneously achieving the error correction capability of the code is of interest, however, the presently studied schemes based on block error correction codes may require relatively very low code rate codes resulting in relatively very poor bandwidth efficiency at relatively high number of carriers as concluded by H. Ochiai and H. Imai in their teachings. In the precoding techniques proposed earlier the OFDM modulation symbol vector X(k) is pre multiplied by a fixed orthogonal matrix P resulting in the transformed symbol vector Xp(k)=PX(k). The inverse Fourier transform of the transformed symbol vector provides the OFDM signal vector x(k) for the transmission. The precoding matrix P is signal independent and is known to the receiver. The orthogonal transforms that have been used in the prior art are the discrete Hartley transform (DHT), discrete cosine transform, and the Walsh Hadamard transform (WHT).
The prior methods of the PAPR reduction provide some improvement in the PAPR especially for low order modulation schemes such as the QPSK modulation. However, for high order modulation such as 64 QAM or 256 QAM and for relatively large number of subcarriers N, most of the prior methods provide only a limited reduction in the PAPR with the resulting PAPR significantly higher compared to that for the case of single carrier modulation. Some of the prior schemes have poor bandwidth efficiency, while others require extensive computational effort. It is desirable to have PAPR reduction systems and methods that achieve a PAPR that is comparable to that for the case of single carrier modulation thus almost completely eliminating the PAPR penalty arising from the use of multi carrier modulations methods such as the OFDM system, have high bandwidth efficiency, are computationally efficient and provide for a tradeoff between the PAPR performance and the computational requirements. The systems and methods of this invention possess these and various other benefits.